what is the special thing about a "harvest moon" then? Is it really closer to earth than usual?

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Yes, it actually appears 12% bigger due to its slightly oblong orbit around Earth. It was a timepiece for early farmers to let them know of the fall equinox, and a symbol for early Pagan religions, since most of the Pagan calendars were moon-based.

The moon closest to the Equinox is the Harvest Moon. Occasionally when this falls in October, the September moon becomes the "Corn" or "Barley" Moon.